Prog pretty much got it.....the body is rounded, there is a deep cutaway for fret access, and not everyone likes a single cut look, so they make a cutaway on the upper part too. the horn just so happened to be in a good place to stick a strap.

there are some other styles, but more people just prefer the look of the "normal" shape, and the others might not feel right, look right, or might have odd balance.